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Chapter 12

Lubrication and

Journal Bearings

Lecture Slides

Chapter Outline

Shigley’s Mechanical Engineering Design

Types of Lubrication

Hydrodynamic

Hydrostatic

Elastohydrodynamic

Boundary

Solid film

Viscosity

Shear stress in a fluid is proportional to the rate of change of

velocity with respect to y

m is absolute viscosity, also called dynamic viscosity

Shigley’s Mechanical Engineering Design Fig. 12–1

Viscosity

For most lubricating fluids, the rate of shear is constant, thus

Fluids exhibiting this characteristic are called Newtonian fluids

Units of Viscosity

Units of absolute viscosity

◦ ips units: reyn = lbf·s/in2

◦ SI units: Pa·s = N·s/m2

◦ cgs units: Poise =dyn·s/cm2

cgs units are discouraged, but common historically in lubrication

Viscosity in cgs is often expressed in centipoise (cP), designated

Conversion from cgs to SI and ips:

Units of Viscosity

In ips units, the microreyn (mreyn) is often convenient.

The symbol m' is used to designate viscosity in mreyn

Measurement of Viscosity

Saybolt Universal Viscosimeter used to measure viscosity

Measures time in seconds for 60 mL of lubricant at specified

temperature to run through a tube 17.6 mm in diameter and 12.25

mm long

Result is kinematic viscosity

Unit is stoke = cm2/s

Using Hagen-Poiseuille law kinematic viscosity based on seconds

Saybolt, also called Saybolt Universal viscosity (SUV) in seconds

where Zk is in centistokes (cSt) and t is the number of seconds

Saybolt

Measurement of Viscosity

In SI, kinematic viscosity n has units of m2/s

Conversion is

Eq. (12–3) in SI units,

To convert to dynamic viscosity, multiply n by density in SI units

where r is in kg/m3 and m is in pascal-seconds

Comparison of Absolute Viscosities of Various Fluids

Petroff’s Lightly Loaded Journal Bearing

Petroff’s Equation

Important Dimensionless Parameters

Some important dimensionless parameters used in lubrication

◦ r/c radial clearance ratio

◦ mN/P

◦ Sommerfeld number or bearing characteristic number

Interesting relation

Stable Lubrication

To the right of AB, changes in

conditions are self-correcting

and results in stable lubrication

To the left of AB, changes in

conditions tend to get worse

and results in unstable

lubrication

Point C represents the

approximate transition between

metal-to-metal contact and

thick film separation of the

Common design constraint for

point B,

Fig. 12–4

Thick Film Lubrication

Formation of a film

Center of journal at O

Center of bearing at O'

Eccentricity e

Minimum film thickness h0

occurs at line of centers

Film thickness anywhere is h

Eccentricity ratio

Partial bearing has b < 360

Full bearing has b = 360

Fitted bearing has equal radii

of bushing and journal

Nomenclature of a Journal Bearing

Fig. 12–6

Hydrodynamic Theory

Present theory originated with experimentation of Beauchamp

Tower in early 1880s

Pressure Distribution Curves of Tower

Fig. 12–8

Reynolds Plane Slider Simplification

Reynolds realized fluid films were so thin in comparison with

bearing radius that curvature could be neglected

Replaced curved bearing with flat bearing

Called plane slider bearing

Derivation of Velocity Distribution

Velocity Distribution

Velocity distribution superposes parabolic distribution onto linear

distribution

When pressure is maximum, dp/dx = 0 and u = (U/h) y

Derivation of Reynolds Equation

Reynolds Equation

Classical Reynolds equation for one-dimensional flow, neglecting

side leakage,

With side leakage included,

No general analytical solutions

One important approximate solution by Sommerfeld,

Design Considerations

Variables either given or under control of designer

Dependent variables, or performance factors

Significant Angular Speed

Angular speed N that is significant to hydrodynamic film bearing

performance is

Trumpler’s Design Criteria

Trumpler, a well-known bearing designer, recommended a set of

design criteria.

Minimum film thickness to prevent accumulation of ground off

surface particles

Maximum temperature to prevent vaporization of lighter lubricant

components

Maximum starting load to limit wear at startup when there is

metal-to-metal contact

Minimum design factor on running load

The Relations of the Variables

Albert Raymondi and John Boyd used an iteration technique to

solve Reynolds’ equation.

Published 45 charts and 6 tables

This text includes charts from Part III of Raymondi and Boyd

◦ Assumes infinitely long bearings, thus no side leakage

◦ Assumes full bearing

◦ Assumes oil film is ruptured when film pressure becomes zero

Viscosity Charts

Viscosity is clearly a function of temperature

Viscosity charts of common lubricants are given in Figs. 12–12

through 12–14

Raymondi and Boyd assumed constant viscosity through the

loading zone

Not completely true since temperature rises as work is done on the

lubricant passing through the loading zone

Use average temperature to find a viscosity

Viscosity-Temperature Chart in U.S. Customary Units

Fig. 12–12

Viscosity-Temperature Chart in Metric Units

Fig. 12–13

Viscosity-Temperature Chart for Multi-viscosity Lubricants

Fig. 12–14

Curve Fits for Viscosity-Temperature Chart

Approximate curve fit for Fig. 12–12 is given by

Table 12–1

Notation of Raimondi and Boyd

Polar diagram of the film

pressure distribution showing

notation used by Raimondi and

Fig. 12–15

Minimum Film Thickness and Eccentricity Ratio

Fig. 12–16

Position of Minimum Film Thickness

Fig. 12–17

Coefficient of Friction Variable

Flow Variable

Flow Ratio of Side Flow to Total Flow

Fig. 12–20

Maximum Film Pressure

Fig. 12–21

Terminating Position of Film

Fig. 12–22

Example 12–1

Example 12–2

Example 12–3

Example 12–4

Finding Temperature Rise from Energy Considerations

Fig. 12–23

Combined Temperature Rise Chart

Interpolation Equation

Raimondi and Boyd provide interpolation equation for l/d ratios

other than given in charts

Steady-State Conditions in Self-Contained Bearings

Previous analysis assumes lubricant carries away all enthalpy

increase

Bearings in which warm lubricant stays within bearing housing are

called self-contained bearings

Heat is dissipated from the housing to the surroundings

Heat Dissipated From Bearing Housing

Heat given up by bearing housing

Overall Coefficient of Heat Transfer

Overall coefficient of radiation and convection depends on

material, surface coating, geometry, roughness, temperature

difference between housing and surroundings, and air velocity

Some representative values

Difference in Housing and Ambient Temperatures

The difference between housing and ambient temperatures is

given by

Table 12–2

Housing Temperature

Bearing heat loss to surroundings

Housing surface temperature

Heat Generation Rate

Example 12–5

Effect of Clearance on Example Problems

Some performance characteristics from Examples 12–1 to 12–4,

plotted versus radial clearance

Clearance

Temperature Limits

Pressure-Fed Bearings

Temperature rise can be reduced with increased lubricant flow

Pressure-fed bearings increase the lubricant flow with an external

Common practice is to use circumferential groove at center of

bearing

Effectively creates two half-bearings

Fig. 12–27

Flow of Lubricant From Central Groove

Derivation of Velocity Equation with Pressure-Fed Groove

Distribution of Velocity

Side Flow Notation

Fig. 12–30

Derivation of Side Flow with Force-fed Groove

Characteristic Pressure

The characteristic pressure in each of the two bearings that

constitute the pressure-fed bearing assembly is

Typical Plumbing with Pressure-fed Groove

Derivation of Temperature Rise with Pressure-Fed Groove

Example 12–6

Typical Range of Unit Loads for Sleeve Bearings

Table 12–5

Some Characteristics of Bearing Alloys

Table 12–6

Bearing Types

Fig. 12–32

Fig. 12–33

Typical Groove Patterns

Fig. 12–34

Thrust Bearings

Fig. 12–35

Pressure Distribution in a Thrust Bearing

Fig. 12–36

Flanged Sleeve Bearing

Flanged sleeve bearing can take both radial and thrust loads

Not hydrodynamically lubricated since clearance space is not

wedge-shaped

Fig. 12–37

Boundary-Lubricated Bearings

Relative motion between two surfaces with only a partial lubricant

film (not hydrodynamic) is called boundary lubrication or thin-film

lubrication.

Even hydrodynamic lubrication will have times when it is in thin-

film mode, such as at startup.

Some bearings are boundary lubricated (or dry) at all times.

Such bearings are much more limited by load, temperature, and

speed.

Limits on Some Materials for Boundary-Lubricated Bearings

Table 12–7

Linear Sliding Wear

Fig. 12–38

Wear Factors in U.S. Customary Units

Table 12–8

Coefficients of Friction

Table 12–9

Wear Equation with Practical Modifying Factors

It is useful to include two modifying factors in the linear wear

equation

◦ f1 to account for motion type, load, and speed (Table 12-10)

◦ f2 to account for temperature and cleanliness conditions (Table

12-11)

Motion-Related Factor f1

Shigley’s Mechanical Engineering Design Table 12–10

Environmental Factor f2

Table 12–11

Pressure Distribution on Boundary-Lubricated Bearing

Nominal pressure is

Pressure distribution is given by

Vertical component of p dA is

Integrating gives F,

Fig. 12–39

Pressure and Velocity

Using nominal pressure,

Velocity in ft/min,

Gives PV in psi·ft/min

Note that PV is independent of D

Bushing Wear

Combining Eqs. (12–29), (12–31), and (12–27), an expression for

bushing wear is

Length/Diameter Ratio

Recommended design constraints on length/diameter ratio

Example 12–7

Fig. 12–40

Example 12–7

Table 12–12

Example 12–7

Temperature Rise for Boundary-Lubrication

Example 12–8

Table 12–13

Example 12–8

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